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Leave it to the Astros, a team that's spent the last few years sending fans running to the record books, to the legal dictionary, and occasionally to the therapist, to be the team that in 2014 is sending us back to economics class.

Their general manager, Jeff Luhnow, has both an undergraduate business degree and a Kellogg MBA. Their assistant GM, David Stearns, came from the salary arbitration and collective bargaining team at MLB headquarters. Down the depth chart, their baseball operations analyst, Brandon Taubman, came from the derivatives trading world. Hell, their analogue of a traveling secretary (on this team a more comprehensive “manager of team operations”), Dan O’Neill, per his bio:

…spent seven years in the hedge fund industry with Mesirow Advanced Strategies, Inc. and as partner and chief operating officer of Oak Street Capital Management, LLC in Chicago, IL. Dan holds a B.A. from the University of Illinois and an MBA from the University of Chicago Graduate School of Business.

So it’s not at all a surprise that with the Jon Singleton contract this week, they were the team that was issuing the flashbacks to sitting in the back row of economics class.

And if I remember correctly, I was at the time the one playing the role of former Astro Bud Norris, who was critical of the deal that guaranteed Singleton $10 million but potentially did so at the expense of his upside.

1. The St. Petersburg Paradox and marginal value
Among several economics lessons that can be imparted from the Singleton extend-and-promote deal and the reaction to it is that of risk aversion. If you’re risk-neutral—in other words, you attach no value to certainty or to lowering the variance of your outcome—you’re on Norris’ side. You hate this deal. The expected return for Singleton, weighting all outcomes by their likelihood, is probably above what he is going to make.

I tried so hard to be risk-neutral. As a gambler, it’s a point of pride to figure expected values and go based solely on those. Hedging and other strategies to try to lower variance usually come at high cost. Ultimately, though, I was convinced that there is no such thing as being risk-neutral and that considering contracts like these on expected earnings is a silly way to go.

If you aren’t convinced, consider a game called the St. Petersburg Paradox, which has nothing to do with rationalizing the apparent impossibility that the Rays would have the worst record in the American League.

The game: I’m going to flip a coin. If it’s heads, you get $1 and the game ends. If it’s tails, I flip again. If it’s heads that time, you get $2 and the game ends, if it’s tails, I flip again. If it’s heads the third time, you get $4 and the game ends, if it’s tails, I flip again. And so on. $8, $16, $32…

How much would you be willing to pay to play that game?

No matter what you say, you’re picking something below the expected payout, which you may have known or figured out is infinity. 1*1/2 + 2*1/4 +4*1/8… = ½ + ½ + ½ +… forever.

If you’re willing to pay $100, you will almost certainly lose, even though the expected payout of the game beats yours. It’s an extreme case, but the point is that you don’t value those high ends nearly enough to make you want to figure the excesses of each step into your value of the overall bet. To you, it’s not a sum of ½ forever; it’s a sum that converges to something, since the value of that money to you isn’t really doubling at the end as the probabilities continue halving.

And that’s probably a better way to put Singleton’s situation. The second $10 million to somebody who already has $10 million isn’t worth anything close to what the first $10 million is. Depending on Singleton’s individual situation, there’s a good chance the next $20 million aren’t worth more than guaranteeing the $10 million. Possibly even the next $100 million. In other words, you’d rather have a guaranteed $10 million rather than coin flip for $110.

Dan Brooks yesterday conducted a poll that more resembled a so-called “can’t-miss” prospect’s situation, asking people whether they’d prefer $10 million guaranteed or a 5/6 chance at $25 million (expected value of $20.8 million).

The bigger the difference to you between the first $10 million and the marginal value of the next $10 million is, the smaller your chances of being a bust have to be to make it a good deal for the player to take.

2. Agents’ incentives and game theory
There are enough discussion points within this topic to fill a business school semester. The leverage aspect is one that has been much discussed, with Ben Lindbergh and Sam Miller talking on Effectively Wild about the rightness or wrongness of holding a promotion as a leverage tool against a player who hasn’t made much more than his $200,000 amateur draft signing bonus. And Mike Bates of SB Nation suggested ways of fixing this issue in collective bargaining.

But I wanted to go back to what Norris said, specifically the second half of his statement that he wished Singleton had listened to the union and not his agent.

Given everything just said about Singleton’s priorities and his valuation of money, it doesn’t seem at first like the agent would be driving any of those. Actually, it seems like he would be driving Singleton away from that deal. First of all, the agent’s cut isn’t significant money that would dwarf in importance any bigger payout with uncertainty in the future. Second, and building on the first point, the agent is wealthy, and this would hardly be that first money that guarantees his security.

Why the agent’s incentive is still to take the deal is probably just a guarantee of some business. The player can leave for a different agent any time he wants, and if that happens, the next one-year deal commission goes elsewhere. So in a way, the agent does get some certainty out of this, and does leave behind some potential upside. The risk factors are different—for the player, they’re underperformance and injury, and for the agent, it’s defection. But a players’ ability to change agents, while important and a basic right, is potentially costing players in this regard.

So to review, this is a deal that the player is in favor of, the agent is in favor of, and the union, which represents their interests, is presumably against.

And suddenly it’s back to economics class, this time a game theory application. The union doesn’t like this because in a world of perfect solidarity, these deals don’t happen. Nobody wants anybody else to take this deal because taking the deal waters down the pool. (Presumably, that is. There’s a case to be made that the few players who hit free agency will get more with so few players doing it, but on the whole it’s a believable argument.)

However, as in the prisoner’s dilemma, each individual could be better served by acting in his own interest no matter what anybody else is doing. It’s a little bit difficult to model, since the payoffs aren’t just money, as we saw in the first part of this. Payoffs also have to factor in certainty and other factors that are harder to measure.

So this will be an extreme oversimplification of an industry with dozens of agents and hundreds of players, boiled down to two participants in this dance—you and everyone else.

If everybody goes year to year, let’s say everybody gets 100 in value—just an arbitrary number. But the Jon Singletons of the world and their agents can get a lot of benefit from doing a cheap extension, so they can get up to 110 by doing that. However, that drives down prices, so the average player is hurt by it—by a much smaller amount, but hurt by it nonetheless.

So the chart might look like this, and again, the exact figures aren’t important.

Industry goes year-to-year

Industry does cheap extensions

You go year to year

You get 100, other players get 100

You do cheap extension

You get 110, other players get 98

It now looks like it’s everybody’s best move, assuming the industry has some standard of going year-to-year to deviate from that. But what happens if everybody deviates? Then the pain, if you’re a believer in Norris’ line of thinking, will start to be felt. Everyone’s payoffs drop by a larger amount in the new right column, where these become the norm.

Industry goes year-to-year

Industry does cheap extensions

You go year to year

You get 100, other players get 100

You get 80, other players get 92

You do cheap extension

You get 110, other players get 98

You get 90, other players get 90

The player’s side wants to be in that top left quadrant, where the industry-average payout is highest (100, 100). However, no matter which column we’re in, which is to say no matter what the rest of the industry is doing, if a player’s values prioritize security, he will be better off going year to year. It will in turn make the union as a whole a little worse off, but not enough to make what the player did worse for him.

(We see this sort of model in a lot of business cases, too. One classic example is overfishing the oceans, where the seas as a whole are suffering because everyone’s individual incentive, no matter what the industry is doing, is to overfish, whereas everybody would be better off if nobody overfished.)

Here, whether everybody else is “cooperating” or not, the player’s incentive is to do what’s best for himself and take the extension that offers the player security and the agent his payday. So the world ends up in the lower right quadrant, where everybody is making less (90, 90).

This oversimplified view of the baseball union maps out like a game of collusion, where everybody would be better off if there were an enforceable means of cooperating, which there really isn’t right now.

So what happens when the game is out of whack for one side? When an industry can’t get itself out of that lower right quadrant? The game often changes.

Who was the happiest when cigarette advertising on television was banned? It was actually the cigarette companies. In their game, if the competitors were advertising, it was in their best interest to advertise and not fall behind. If the competitors weren’t, it was in their best interest to advertise and blow them away. So advertising was a dominant strategy. Everybody spent a ton on advertising and sold the same cigarettes as they would have sold if nobody was. Once TV advertising was banned, they could just pocket that money and sell the same number of cigarettes. The rules of the game had changed.

A solution here isn’t so easy. Somehow preventing players from changing agents would get the agents’ priorities back in line with the union’s, but it doesn’t seem all that feasible. And if a player did truly want that security, the conflict would shift to player vs. agent rather than player/agent vs. union.

Maybe they do go that cigarette route and use the next round of CBA negotiations to use something that in the game theory sense, they can’t help themselves from taking. In his piece, Bates suggested not letting players with less than a year of service time sign extensions, which would be one approach.

But if enough people in the union leadership view the world like Norris—and his view is hardly unique—then understanding how the individual incentive outweighs the collective incentive could be as much of a focus as changing the leverage.

Thank you for reading

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The union needs to think less in terms of overall dollars and more in terms of security for those they represent. In this industry, the bottom right quadrant means set-for-life money. More important, that money comes sooner and reaches more players. Injuries and/or failing to perform at the highest level are all too common to turn down set-for-life money. It's important to remember that the union has repeatedly shown it is willing to short change amateurs and MiLB players to make established players richer.
Excellent point, I could not agree more.
Killed it. One of the best articles I've read on this website ever.
What would Singleton have expected to make going year-by-year?

the next 3 years, he'd be basically at the minimum, $0.5M. And if he hadn't signed the deal and gotten promoted immediately, he wouldn't have been eligible for arbitration after 2016 (assuming the Astros would have kept him in the minors until they were sure he wouldn't be super-2 eligible, he would have gotten pretty close to the minimum on 2017. If we assume that Singleton is very good but not great, assume he gets something like $4M-$8m-$10M in arbitration (Paul Goldschmidt is getting $3.1/$5.875/$8.875M for those years in his deal; Freddie Freeman is getting $5.125M/$8.5M/$12.0M). With those numbers, Singleton's salaries look something like:

2014: $0.5M
2015: $0.5M
2016: $0.5M
2017: $0.5M
2018: $4.0M
2019: $8.5M
2020: $12.0M
2021: ? (FA eligible)

So he'd get $6M through 2018, compared to the $10M he's getting with the contract. The Astros only end up saving money in 2020 - Singleton would probably have made ~$27M going year-by-year, which isn't that far above what the contract pays him. Though 2021 ends up being a major bargain for the Astros.

BUT... the above assumes that Singleton pretty much immediately steps up, and remains healthy and productive for the next 6 years. If he struggles, or doesn't live up to expectations, or gets hurt, his expected salaries going year-by-year drop.

the deal is basically neutral through the years that would have been team-controlled anyway. If Singleton is a superstar, the 2021 option could end up costing him $20M compared to what he would have got going year-by-year - but he's FA eligible after that year and will get a mega contract anyway. If Singleton is good but not great for the next 6 years, the 2021 option might cost him $5M. If Singleton sucks and/or gets hurt, the contract makes him $5-6M more than he would have gotten going year-by-year.

I think this was a good deal for both sides. Sure, you can construct a scenario where it costs Singleton a lot of money. but that's not the most likely scenario, IMHO.
It's neutral given that the team would have still avoided Super Two if he hadn't signed the contract, and I think it's that monkeying with the clock / leverage that I think people are reacting to. If they'd called him up when he was ready, and you exchange an arb year for a minimum salary year, the picture changes a bit.

This doesn't go to whether Singleton should or should not have signed the deal, and it's also just one step further from the normal, non-extension-related, service time shenanigans, I.e. I don't know if the Astros are actually acting any worse than any team, and in any event I don't have a good solution to the Super Two problem any more than anyone else does, but it seems worth noting anyway.
"If they'd called him up when he was ready".

This is the implication I keep seeing that I disagree with. A player coming out of rehab and suspension, who was a disaster on the field last year? He wasn't ready earlier in the year, and there's a good argument to be made that he could still be in the minors now, with very little rationalization.

So the monkeying with the clock/leverage argument is based on shaky ground in the first place, in my opinion.
Obviously, the Astros beg to differ with you regarding how ready he was, since they did in fact call him up.

The EXACT minute that they got cost certainty, no less.

They didn't even try to fake anyone out by making him wait even a day.
Norris clearly has an Astros sized axe to grind. He's been nothing but critical and disparaging since he was traded. What I'm not sure about is why anybody cares what Bud Norris has to say. What are his qualifications for judging singleton's contract? Being a current MLB player hardly qualifies one as being the arbiter for another player's financial decisions; especially when given the context of current lifetime earnings.

If singleton excels at the MLB level, he will have cost himself some money. But now he's set regardless of anything else that happens. Very few people have that kind of security. However, excelling at the MLB level is a fairly difficult task. Or so I'm told.

Anyway, fascinating article. Skewed left is my favorite series on the site.
Thanks, and that's definitely fair. Using the Norris quote was more as a setup to talk about the issues because it's something we've heard lots of times before. What he individually thinks about this specific deal, you're right, isn't of that much consequence especially since he does have his own Astros ties that tend to come up.
I didn't mean that as a slam on the introduction. I'm just confused by how much traction that tweet has received. It's nuts that such a ridiculous tweet/opinion has been referred to as having some sort of legitimacy when discussing the merits (or lack thereof) of Singletons contract.
Zachary, there have been other reports of Norris being difficult when he was in Houston, and recently the Chronicle quoted him being a sourpuss towards the Astros again (pretty well-covered story nationally, actually).

Can you shed some light on if Norris was particularly cantankerous when you covered the Astros?
Great article.
Bud Norris is a West Coast guy bitter over being traded to the East Coast and angry over his own financial situation ... in his five years of major league work he has earned $9,650,000 and won't be free until 2016. Union, union, union ....
Zach, just wanted to say this is a great article
To me, this article (and organized sports in general, really) underscores the important interplay between cooperation and competition. If an organized group of individuals goes too far in one direction or the other (too competitive or too cooperative), then change is inevitable (i.e., not sustainable).
Sports are only fun to play and follow if the playing field is relatively flat. In other words, the participants must agree to certain rules that apply to everyone (cooperation) in order for the resulting competition to be interesting.
It's the same deal with more important things like species survival. To take just one example - the one used in this article - the overfishing problem that has resulted from too many people acting in their self-interest will inevitably lead to significant change in humanity's ability to acquire food from the oceans. Humanity, at the very least, must first agree to limit how much can be harvested from the ocean as a whole (cooperation) before letting the competition of best fishing practices play out. Otherwise, the game changes and must be played differently.
Nice job Zach. I really appreciate the economics class essays.
I have a totally unverifiable theory about these extensions, which can accomodate Norris's comments without assuming they are just about sour grapes- That the owners and union are already pretty far along on the next CBA, that it will include some substantial (upward) changes to the current compensation system for players still under team control, and the outline of these changes are already more or less agreed to (but are highly secret and NDA'd as is de rigeur), and they intend on finalizing them before next offseason. Everyone wants peace to continue, the game is swimming in $, and Selig probably wants one last CBA inked or semi-inked before he retires.

If this is the case, then a good chunk of the higher pay teams are 'risking' is money they will probably have to shell out to players under control anyways under the next CBA. As team-friendly as a lot of these deals look, I bet they look a lot better under the next CBA. Regardless of what Norris thinks personally, he is implying that the union is actively advising players generally not to sign these extensions. The union really only needs one star to grind through arbitration to reset the scale upward (like Cabrera did), so my suspicion is that they are telling players "trust us, just wait until the All-Star break before you sign anything" rather than "don't sign the early extension"